In this paper, we propose a novel few-shot optimization with HED-LM (Hybrid Euclidean Distance with Large Language Models) to improve example selection for sensor-based classification tasks. While few-shot prompting enables efficient inference with limited labeled data, its performance largely depends on the quality of selected examples. HED-LM addresses this challenge through a hybrid selection pipeline that filters candidate examples based on Euclidean distance and re-ranks them using contextual relevance scored by large language models (LLMs). To validate its effectiveness, we apply HED-LM to a fatigue detection task using accelerometer data characterized by overlapping patterns and high inter-subject variability. Unlike simpler tasks such as activity recognition, fatigue detection demands more nuanced example selection due to subtle differences in physiological signals. Our experiments show that HED-LM achieves a mean macro F1-score of 69.13$\pm$10.71%, outperforming both random selection (59.30$\pm$10.13%) and distance-only filtering (67.61$\pm$11.39%). These represent relative improvements of 16.6% and 2.3%, respectively. The results confirm that combining numerical similarity with contextual relevance improves the robustness of few-shot prompting. Overall, HED-LM offers a practical solution to improve performance in real-world sensor-based learning tasks and shows potential for broader applications in healthcare monitoring, human activity recognition, and industrial safety scenarios.